Commit 9ce3350a authored by Guillaume Melquiond's avatar Guillaume Melquiond

Prove canonic_exp_{le,ge}_bpow.

parent 3cc94cb2
......@@ -1505,6 +1505,29 @@ now apply Zlt_le_succ.
now apply valid_exp.
Qed.
Lemma canonic_exp_le_bpow :
forall (x : R) (e : Z),
x <> R0 ->
(Rabs x < bpow e)%R ->
(canonic_exp x <= fexp e)%Z.
Proof.
intros x e Zx Hx.
apply monotone_exp.
now apply ln_beta_le_bpow.
Qed.
Lemma canonic_exp_ge_bpow :
forall (x : R) (e : Z),
(bpow (e - 1) <= Rabs x)%R ->
(fexp e <= canonic_exp x)%Z.
Proof.
intros x e Hx.
apply monotone_exp.
rewrite (Zsucc_pred e).
apply Zlt_le_succ.
now apply ln_beta_gt_bpow.
Qed.
Variable rnd : R -> Z.
Context { valid_rnd : Valid_rnd rnd }.
......
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